Which of the following complex will show largest splitting of d-orbitals?

The correct representation in six membered pyranose form for the following sugar [X] is

Highest oxidation state of Mn is exhibited in $\mathrm{Mn_2O_7}$. The correct statements about $\mathrm{Mn_2O_7}$ are

(A) Mn is tetrahedrally surrounded by oxygen atoms.

(B) Mn is octahedrally surrounded by oxygen atoms.

(C) Contains Mn-O-Mn bridge.

(D) Contains Mn-Mn bond.

Choose the correct answer from the options given below :

Which of the following are the example of double salt?

A. $\mathrm{FeSO}_{4} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}$

B. $\mathrm{CuSO}_{4}\cdot 4 \mathrm{NH}_{3} \cdot \mathrm{H}_{2} \mathrm{O}$

C. $\mathrm{K}_{2} \mathrm{SO}_{4} \cdot \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot 24 \mathrm{H}_{2} \mathrm{O}$

D. $\mathrm{Fe}(\mathrm{CN})_{2}\cdot4 \mathrm{KCN}$

Choose the correct answer :

But-2-yne is reacted separately with one mole of Hydrogen as shown below :

A. A is more soluble than B.

B. The boiling point & melting point of A are higher and lower than B respectively.

C. A is more polar than B because dipole moment of A is zero.

D. $\mathrm{Br_2}$ adds easily to B than A.

Identify the incorrect statements from the options given below :

Decreasing order of dehydration of the following alcohols is

25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M $\mathrm{AgNO_3}$ solution when titrated using $\mathrm{K_2CrO_4}$ as an indicator. What is the depression in freezing point of KCl solution of the given concentration? _________ (Nearest integer).

(Given : $\mathrm{K_f=2.0~K~kg~mol^{-1}}$)

Assume 1) 100% ionization and 2) density of the aqueous solution as 1 g mL$^{-1}$

A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of both of them to be same? _____________ min.

The shortest distance between the lines

${{x - 5} \over 1} = {{y - 2} \over 2} = {{z - 4} \over { - 3}}$ and

${{x + 3} \over 1} = {{y + 5} \over 4} = {{z - 1} \over { - 5}}$ is :

Let $S$ denote the set of all real values of $\lambda$ such that the system of equations

$\lambda x+y+z=1$

$x+\lambda y+z=1$

$x+y+\lambda z=1$

is inconsistent, then \sum_\limits{\lambda \in S}\left(|\lambda|^{2}+|\lambda|\right) is equal to

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :

If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is $(\alpha,\beta)$, then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$, is :

If \int_\limits{0}^{1}\left(x^{21}+x^{14}+x^{7}\right)\left(2 x^{14}+3 x^{7}+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n} where $l, m, n \in \mathbb{N}, m$ and $n$ are coprime then $l+m+n$ is equal to ____________.

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.

'$n$' polarizing sheets are arranged such that each makes an angle $45^{\circ}$ with the preceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be $I / 64$. The value of $n$ will be:

Match List I with List II:

Choose the correct answer from the options given below :

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\mathrm{given}, \gamma=\frac{3}{2}\right)$ :

Match List I with List II :

Choose the correct answer from the options given below :

Two equal positive point charges are separated by a distance $2 a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $\mathrm{q}_{0}$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is __________.

A solution of $\mathrm{FeCl_3}$ when treated with $\mathrm{K_4[Fe(CN)_6]}$ gives a prussium blue precipitate due to the formation of :

Identify the incorrect option from the following

At $25^{\circ} \mathrm{C}$, the enthalpy of the following processes are given :

What would be the value of X for the following reaction ? _____________ (Nearest integer)

$\mathrm{H_2O(g)\to H(g)+OH(g)~\Delta H^\circ=X~kJ~mol^{-1}}$

Sum of oxidation states of bromine in bromic acid and perbromic acid is ___________.

(i) $\mathrm{X}(\mathrm{g}) \rightleftharpoons \mathrm{Y}(\mathrm{g})+\mathrm{Z}(\mathrm{g}) \quad \mathrm{K}_{\mathrm{p} 1}=3$

(ii) $\mathrm{A}(\mathrm{g}) \rightleftharpoons 2 \mathrm{~B}(\mathrm{g}) \quad \mathrm{K}_{\mathrm{p} 2}=1$

If the degree of dissociation and initial concentration of both the reactants $\mathrm{X}(\mathrm{g})$ and $\mathrm{A}(\mathrm{g})$ are equal, then the ratio of the total pressure at equilibrium $\left(\frac{p_{1}}{p_{2}}\right)$ is equal to $\mathrm{x}: 1$. The value of $\mathrm{x}$ is _____________ (Nearest integer)

The density of $3 \mathrm{M}$ solution of $\mathrm{NaCl}$ is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$. Molality of the solution is ____________ $\times 10^{-2} \mathrm{~m}$. (Nearest integer).

Given: Molar mass of $\mathrm{Na}$ and $\mathrm{Cl}$ is $23$ and $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively.

Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$. Then \sum_\limits{x \in S} 2 \sin ^{-1}\left(x^{2}-1\right) is equal to :

Let $R$ be a relation on $\mathbb{R}$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$. Then $R$ is

Let $f(x) = 2x + {\tan ^{ - 1}}x$ and $g(x) = {\log _e}(\sqrt {1 + {x^2}} + x),x \in [0,3]$. Then

The area enclosed by the closed curve $\mathrm{C}$ given by the differential equation

$\frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0$ is $4 \pi$.

Let $P$ and $Q$ be the points of intersection of the curve $\mathrm{C}$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $\mathrm{C}$ intersect $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $R S$ is :

The remainder, when $19^{200}+23^{200}$ is divided by 49 , is ___________.

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.

If earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_{e}}{3} \sqrt{x} \mathrm{~ms}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $\mathrm{P}$, where $v_{e}$ is escape velocity on earth. The value of $x$ is

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

A small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}$. The value of work done will be __________ J.

Match List I with List II

Choose the correct answer from the options given below :

In the following reaction, 'A' is

Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s$^{-1}$. The number of following statements which is/are $\underline {\mathrm{true}}$ about the emitted radiation is ____________.

Given : $\mathrm{h=6\times10^{-34}~J~s,m_e=9\times10^{-31}~kg}$.

(A) The de-Broglie wavelength of the electron emitted is 666.67 nm.

(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube.

(C) The cathode rays start from cathode and move towards anode.

(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

At what pH, given half cell $\mathrm{MnO_{4}^{-}(0.1~M)~|~Mn^{2+}(0.001~M)}$ will have electrode potential of 1.282 V? ___________ (Nearest Integer)

Given $\mathrm{E_{MnO_4^ - |M{n^{2 + }}}^o}=1.54~\mathrm{V},\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059\mathrm{V}$

The total number of chiral compound/s from the following is ______________.

The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :

If the center and radius of the circle $\left| {{{z - 2} \over {z - 3}}} \right| = 2$ are respectively $(\alpha,\beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to :

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that f^{\prime}(x)+f(x)=\int_\limits{0}^{2} f(t) d t. If $f(0)=e^{-2}$, then $2 f(0)-f(2)$ is equal to ____________.

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12 A$ is equal to ____________.

Find the magnetic field at the point $\mathrm{P}$ in figure. The curved portion is a semicircle connected to two long straight wires.

The equivalent resistance between $A$ and $B$ of the network shown in figure;

A steel wire with mass per unit length $7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ is under tension of $70 \mathrm{~N}$. The speed of transverse waves in the wire will be:

An object moves with speed $v_1,v_2$ and $v_3$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

A child stands on the edge of the cliff $10 \mathrm{~m}$ above the ground and throws a stone horizontally with an initial speed of $5 \mathrm{~ms}^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be $\mathrm{ms}^{-1}$ (given, $g=10 \mathrm{~ms}^{-2}$ ).

$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^{2}}{a}$, will be:

A mercury drop of radius $10^{-3}~\mathrm{m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45~\mathrm{Nm}^{-1}$. The gain in surface energy is :

A light of energy $12.75 ~\mathrm{eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi} \times 10^{-17} ~\mathrm{eVs}$. The value of $x$ is ___________ (use $h=4.14 \times 10^{-15} ~\mathrm{eVs}, c=3 \times 10^{8} \mathrm{~ms}^{-1}$ ).

A thin cylindrical rod of length $10 \mathrm{~cm}$ is placed horizontally on the principle axis of a concave mirror of focal length $20 \mathrm{~cm}$. The rod is placed in a such a way that mid point of the rod is at $40 \mathrm{~cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{x}{3} \mathrm{~cm}$. The value of $x$ is _____________.

A series LCR circuit is connected to an ac source of $220 \mathrm{~V}, 50 \mathrm{~Hz}$. The circuit contain a resistance $\mathrm{R}=100 ~\Omega$ and an inductor of inductive reactance $\mathrm{X}_{\mathrm{L}}=79.6 ~\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $\mu \mathrm{F}$.

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length $60 \mathrm{~cm}$. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is __________ $\mathrm{ms}^{-1}$. (Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$)

Resonance in carbonate ion $\left(\mathrm{CO}_{3}{ }^{2-}\right)$ is

Which of the following is true?

Number of isomeric compounds with molecular formula $\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}$ which (i) do not dissolve in $\mathrm{NaOH}$ (ii) do not dissolve in $\mathrm{HCl}$. (iii) do not give orange precipitate with 2,4-DNP (iv) on hydrogenation give identical compound with molecular formula $\mathrm{C}_{9} \mathrm{H}_{12} \mathrm{O}$ is ____________.

Let $S = \left\{ {x:x \in \mathbb{R}\,\mathrm{and}\,{{(\sqrt 3 + \sqrt 2 )}^{{x^2} - 4}} + {{(\sqrt 3 - \sqrt 2 )}^{{x^2} - 4}} = 10} \right\}$. Then $n(S)$ is equal to

Let f(x) = \left| {\matrix{ {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \sin 2x} \cr } } \right|,\,x \in \left[ {{\pi \over 6},{\pi \over 3}} \right]\(. If \)\alpha\( and \)\beta\( respectively are the maximum and the minimum values of \)f, then

If $y=y(x)$ is the solution curve of the differential equation

$\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1$, then $y\left(\frac{\pi}{6}\right)$ is equal to

Let $a_{1}=8, a_{2}, a_{3}, \ldots, a_{n}$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is ___________.

$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$ and $D(4,5,0),|\lambda| \leq 5$ are the vertices of a quadrilateral $A B C D$. If its area is 18 square units, then $5-6 \lambda$ is equal to __________.

If $f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)$ and $g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)$, then the value of $f(4)-g(4)$ is equal to ____________.

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_{I}, E_{I I}$ and $E_{I I I}$ are:

Match List - I with List - II :

Choose the correct answer from the options given below :

Given below are two statements:

Statement I: Acceleration due to gravity is different at different places on the surface of earth.

Statement II: Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

A block of mass $5 \mathrm{~kg}$ is placed at rest on a table of rough surface. Now, if a force of $30 \mathrm{~N}$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50 \mathrm{~m}$ in an interval of time $10 \mathrm{~s}$. Coefficient of kinetic friction is (given, $g=10 \mathrm{~ms}^{-2}$):

The mass of proton, neutron and helium nucleus are respectively $1.0073~u,1.0087~u$ and $4.0015~u$. The binding energy of helium nucleus is :

The average kinetic energy of a molecule of the gas is

A charge particle of $2 ~\mu \mathrm{C}$ accelerated by a potential difference of $100 \mathrm{~V}$ enters a region of uniform magnetic field of magnitude $4 ~\mathrm{mT}$ at right angle to the direction of field. The charge particle completes semicircle of radius $3 \mathrm{~cm}$ inside magnetic field. The mass of the charge particle is __________ $\times 10^{-18} \mathrm{~kg}$

A certain pressure '$\mathrm{P}$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01 \%$ whereas the liquid gets compressed to $0.03 \%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ____________.

The amplitude of a particle executing SHM is $3 \mathrm{~cm}$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is: __________ $\mathrm{cm}$